Grilled Figs With Honeyed Mascarpone

12 ripe, plump black figs
1/4 cup plus 1 tablespoon dark honey, such as buckwheat or pine
1 3-inch sprig fresh rosemary, plus additional sprigs for garnish
4 ounces mascarpone cheese
1 tablespoon rum
1 lemon, zested

Slice the figs in half lengthwise and arrange on a plate or platter. Heat 1/4 cup honey and the rosemary sprig in a small saucepan over medium heat. Bring to a simmer and lower the heat. Don't walk away; watch it carefully so that it does not boil over or scorch. Let the honey simmer for about 2 minutes, then turn off the heat. Quickly but carefully, dip the fig halves in the hot honey. Use a fork, small tongs, or your fingers. Make sure to at least lightly coat their cut side. Place the dipped fig halves back on the platter.

In a medium bowl, use an immersion blender or hand mixer to whip the mascarpone with the remaining tablespoon of honey, the rum, and the lemon zest. Whip until the cheese is frothy and aerated. Cover the bowl and put the cheese in the refrigerator.

Heat a gas grill to medium-hot. When it is quite hot, arrange all the figs on the grill, cut side down. It is best to put them over indirect heat. As soon as you finish putting out all the figs, cut side down, flip them over, starting with the figs that have been on the grill the longest. They should have developed dark grill marks, and the honey should be getting brown and caramelized. Flip all the figs over and let them sit on the grill for a few more moments. They should have grill marks on both sides, and be just warmed through. Remove them to a platter.

Note: The grilled figs can be made an hour or more ahead of serving time. Place them cut side up on a platter and, when ready to serve, microwave for one or two 30-second bursts to warm them through.

When ready to serve, spread a smear of mascarpone cheese on a dessert plate. Arrange six fig halves on top of the cheese, and place an extra dollop of cheese to the side. Add a rosemary sprig for garnish and serve while the figs are still warm.

Spread mascarpone on each fig half and eat with your fingers